A020345 Smallest Fibonacci number beginning with n.

0, 1, 2, 3, 4181, 5, 610, 75025, 8, 987, 10946, 1134903170, 121393, 13, 144, 1597, 165580141, 17711, 1836311903, 196418, 20365011074, 21, 225851433717, 233, 24157817, 2584, 267914296, 27777890035288, 28657, 2971215073, 308061521170129, 317811

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• base

Comments

The graph of the indices A020344 is much more interesting. - T. D. Noe, Apr 02 2014

a(1382) is the first term with > 1000 digits (1004). - Michael S. Branicky, Jul 08 2022

Examples

			a(4) = 4181 is a Fibonacci number starting with 4.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..1389 (terms 1..400 from T. D. Noe)
• Ron Knott, Every number starts some Fibonacci Number, The Mathematical Magic of the Fibonacci Numbers.

Crossrefs

Cf. A000045, A020344, A023183, A023184.

Programs

Mathematica

nn = 31; t = tn = Table[0, {nn}]; found = 0; n = 0; While[found < nn, n++;  f = Fibonacci[n]; d = IntegerDigits[f]; i = 1; While[i <= Length[d], k = FromDigits[Take[d, i]]; If[k > nn, Break[]]; If[t[[k]] == 0, t[[k]] = f; tn[[k]] = n; found++]; i++]]; t = Join[{0}, t] (* T. D. Noe, Apr 02 2014 *)

Python

def aupton(nn):
    ans, f, g, k = dict(), 0, 1, 0
    while len(ans) < nn+1:
        sf = str(f)
        for i in range(1, len(sf)+1):
            if int(sf[:i]) > nn:
                break
            if sf[:i] not in ans:
                ans[sf[:i]] = f
        f, g, k = g, f+g, k+1
    return [int(ans[str(i)]) for i in range(nn+1)]
print(aupton(31)) # Michael S. Branicky, Jul 08 2022

Formula

a(n) = A000045(A020344(n)).